Towards pore network modelling of spontaneous imbibition: contact angle dependent invasion patterns and the occurrence of dynamic capillary barriers

Abstract

Imbibition is an important process encountered in many porous media applications. At the pore scale, pore network models (PNM) are computationally efficient and can model drainage accurately. However, using PNM to model imbibition still remains a challenge due to the complexities encountered in understanding pore-scale flow phenomena related to pore body filling (PBF) and snap-off along with the relative competition between these events. In this work, we use direct numerical simulations (DNS) to revisit the basic principles of PBF in a two-dimensional synthetic pore geometry. We notice that PBF during spontaneous imbibition is dependent on several parameters such as shape of the transition zone, contact angle and the fluid properties like density. The interactions between these parameters are investigated in a quantitative manner. We demonstrate the existence of a critical contact angle θ c and a barrier contact angle θ b . θ c depends on the shape of the pore geometry, whereas θ b depends on the pore geometry, contact angle and fluid properties. For a system comprising of light fluids, θ b is only slightly larger than θ c ; whereas for a system occupied by dense fluids, θ b is notably larger than θ c . The contact angle of the wetting phase θ in relation to θ c and θ b decides if the wetting phase can imbibe a pore body. Imbibition always occurs if θ < θ c . For θ > θ c , we observe capillary barrier zones in which capillary forces accompany viscous forces to resist spontaneous imbibition. For this case, we observe smooth transition of the meniscus curvature while the meniscus enters and exits capillary barrier zones. For θ c ≤ θ ≤ θ b , inertia assists the wetting phase to overcome resisting forces and imbibe the pore space. For θ > θ b , the resisting forces dominate over inertia so that the wetting phase cannot imbibe the pore space. For the synthetic pore geometries investigated, we provide analytical and semi-analytical expressions to determine θ c and the position of capillary barrier zones respectively. The barrier contact angle θ b is computed numerically for several inertial systems and for various shapes of the synthetic pore geometry. The results of this quantitative analysis can be utilised to improve the existing pore filling rules and predictive capabilities of PNM used for two-phase flows.

Computational Microfluidics for Geosciences

“…Most of computational microfluidics developments so far have been devoted to solve the Navier-Stokes equations under single (Spanne et al, 1994;Bijeljic et al, 2013;Guibert et al, 2015; and two-phase flow conditions (Horgue et al, 2013;Raeini et al, 2014;Graveleau et al, 2017;Maes and Soulaine, 2018a;Pavuluri et al, 2020). Flow in geological porous media, however, has the distinctive feature to interact chemically with the solid walls.…”

“…Alternatively, computational microfluidics can be used to directly solve the flow and transport equations within the pore-space and compute the desired upscaled properties. Although it is often restricted to small micro-CT images (<300 3 voxels) or to single-phase flow due to high computing cost, computational microfluidics is also well-suited to investigate pore-to-pore physics (Ferrari and Lunati, 2014;Pavuluri et al, 2020) with the objective of improving upscaling techniques (e.g., pore entry pressure for pore network modeling). A major asset of microfluidics is the ability to design well-controlled experiments and obtain high-resolution measurements-both in space and time-of the velocity fields (Roman et al, 2016), phase distribution, film thickness (Roman et al, 2017), aqueous species concentrations (Chang et al, 2017), and mapping in mineral changes (Poonoosamy et al, 2020).…”

Investigation of the Effect of Capillary Barrier on Water–Oil Movement in Water Flooding

“…The complex capillary pressure distribution and configuration of fluid during displacement in highly heterogeneous porous media were measured via image processing methods and the results can facilitate better understanding of fluid displacement process [29]. Pavuluri [30] identified the critical contact angle θ c in pore network models using direct numerical simulations and found that the capillary barrier zones in which capillary forces along with viscous forces resist spontaneous imbibition were observed when contact angle θ exceeds θ c . Factors affecting capillary effect in two-phase flow include the effect of porous media properties (pore-throat size, grain size, heterogeneity, fracture), the effect of fluid saturation and properties, and the effect of external factors (domain size, surfactant, temperature), which are reviewed extensively in the literature [31].…”

GeoChemFoam: Direct Modelling of Multiphase Reactive Transport in Real Pore Geometries with Equilibrium Reactions

“…While numerical modelling of multiphase flow (Pavuluri et al 2020;Ferrari et al 2015;Zhao et al 2019) and single-phase reactive transport (Szymczak and Ladd 2009;Soulaine et al 2017;Oliveira et al 2020) in pore-scale geometries have been extensively investigated independently, few studies have attempted to model the coupling between the two. Raoof et al (2013) used a pore network model to simulate reactive transport in variably saturated porous media.…”